In this work, starting from the well-accepted relations in literature, we introduce a new formalism to compute the astrometric membership probabilities for sources in star clusters, and we provide an application to the case of the open cluster M 37. The novelty of our approach is a refined - and magnitude- dependent - modelling of the parallax distribution of the field stars. We employ the here-derived list of members to estimate the cluster's mean systemic astrometric parameters, which are based on the most recent Gaia's catalogue (EDR3).

Cone search capability for table J/MNRAS/511/4702/table (M 37 star's cluster with their P_memb_ computed with the formalism presented in this work)